﻿<p>
  In portfolio theory, the riskiness of an asset is often measured by the variance (or standard deviation) of its returns. Risk-averse investors do not want their wealth to fluctuate wildly.
</p>

<p>
  Risk aversion can be illustrated with a simple example. Which of the following assets do you prefer?
</p>

<ul>
    <li>Asset A pays $200 or $0 with 50% probability each.</li>
    <li>Asset B pays $400 or &minus;$200 (i.e. you lose $200) with 50% probability each.</li>
</ul>

<p>
  The expected payouts of A and B are:
</p>

\[ \mathbb{E}(A) = 0.5 \times 200 + 0.5 \times 0 = 100 \]
\[ \mathbb{E}(B) = 0.5 \times 400 + 0.5 \times (-200) = 100 \]

<p>
  The standard deviation of their payouts are:
</p>
\[ \sigma_A = \sqrt{0.5(200-100)^2 + 0.5(0-100)^2} = 100 \]
\[ \sigma_A = \sqrt{0.5(400-100)^2 + 0.5(-200-100)^2} = 300 \]

<p>
  If you are an risk seeker, you may choose asset B, because you can potentially get a higher payout. MPT assumes that investors prefer asset A since both assets have the same expected payout, but asset A has less risk.
</p>
